Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays

•A within-host chikungunya virus infection model with two delays is proposed.•Maturation delay for newly produced virus does not affect the dynamics.•Antigenic stimulation delay can change the stability of endemic state.•Hopf bifurcation can explain the persistence of virus even after subsiding of viremia.

In this paper, a within-host chikungunya virus infection model with two delays is considered. The basic reproductive number R0 is formulated. If R0<1, the virus-free equilibrium is globally asymptotically stable and the disease always dies out. If R0>1, the global stability of the unique endemic equilibrium E1 is proved for the case without the time delay of antigenic stimulation, which can change the stability of E1 and lead to the existence of Hopf bifurcation. Furthermore, explicit formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are established. Finally, some numerical simulations are presented to illustrate the results.